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This sentence uses $ delimiters to show math inline: $\sqrt{3x-1}+(1+x)^2$

The Cauchy-Schwarz Inequality

$$\left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right)$$

This expression uses \$ to display a dollar sign: $\sqrt{$4}$

To split $100 in half, we calculate $100/2$